Broad band amplifier



Jan. 23, 1945. H w BQDE 2,367,711

BROAD BAND AMPLIFIER Filed Jan. 12, 1943 3 Sheets-Sheet l FIG. 7

l/E/V TOR H. 146 5005 ATTORNEY Jan. 23, w BODE BROAD BAND AMPLIFIERFiled Jan. 12, 1945 3 Sheets-Sheet 2 0: 5 FIG. 9

LOG. FREQ.

LOG. FREQ.

lA/l/E/VTOR H W. 5005 BV 1.06. FREQ. '2

Jan. 23, 1945. I BQDE 2,367,711

BROAD BAND AMPLIFIER Filed Jan. 12, 1945 5 Sheets-Sheet 3 FIG. /3

v 6 PHASE SHIFT k i 5 E E e S 5 L06. FREQ.

LOOP 64 IN db ATTENUA 7/0/V db LO 6. FREQ.

//v VE/V TO I? H W 8005 ATTORNEY Patented Jan. 23,

2,387,711 BROAD BAND AMPLIFIER Hendrik W. Bode, New York, N. Y.,assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y.,a corporation of New York Application January 12, 1943, Serial No.472,123

Claims.

The present invention relates to broad band amplifiers using negativefeedback to secure such well-known advantages as increase of linearityand stability of amplification.

It is known that the degree of improvement in such factors as linearityand gain stability is roughly proportional to the amount of feedbackused so long as the feedback is large. A practical limitation is placedupon the amount of feedback that can be used in the transmissionfrequency band by the tendency of the amplifier to sing at some highfrequency well above the band. This presents a problem of so controllingthe gain and phase shift around the feedback loop as to secure themaximum amount of feedback in the useful band while maintaining asuitable margin against singing at potential singing frequencies. MyPatent 2,123,178, granted July 12, 1938. discloses how to control thetransmission characteristics around the feedback loop to insure completestability against singing without the sacrifice of gain in the usefulband. Amplifiers designed in accordance with the teachings of thatpatent are referred to as completely or absolutely stable amplifiers.

As an alternative to providing a margin against singing, it has beensuggested that this margin could be sacrificed in the interest ofincreased useful gain provided the sing amplitude is held down to so lowa level that no harmful overloading is produced by it. It was proposedto operate a gain control or a loss device capable of responding to asinging condition to control the net gain around the feedback loop insuch manner as to oppose an increase of the sing amplitude above somepredetermined value too low to produce harmful overloading.

The present invention represents an improvement over the latter type ofamplifier, and achieves a marked increase in useful gain and feedbackfactor by controlling both the gain and phase shift characteristics ofthe feedback loop in response to the singing condition. In my priorpatent it was shown how to control the rate of diminution of themagnitude of the feedback factor (as) in the cut-oil ranges, especiallyin the high frequency cut-off range above the useful band, to provideoptimum attenuation and phase characteristics for the purpose ofsecuring maximum feedback in the used band with minimum loss of usefulfrequency range and with complete stability against singing. Arestriction was necessarily placed upon the rate of diminution of themagnitude of the feedback factor with increasing frequency in thecut-off region by the assumed requirement that the circuit be completelystable against singing. In accordance with the present invention, thisrestriction is observed at all gain levels below that at which the singcondition beginsso that the circuit remains completely stable whilebeing turned on or when either momentarily passing through low gainlevels or kept at low gain level indefinitely, but as soon as a singcondition is established with increasing gain the invention provides formore or less radically reshaping the course of the feedback factor overthe cut-off region in such manner as to increase in corresponding degreethe magnitude of the feedback factor-in the useful range. This type ofcontrol enables a much greater feedback ratio to be obtained over theuseful band than could be had with the mentioned prior art types of singcontrol.

In accordance with a feature of the present invention, a network isincluded at a suitable point in the feedback loop, adapted to have itsattenuation and phase characteristics changed under control of a currentresponsive device forming an element of the network. The arrangement issuch that this device is affected by the sing current and under controlof the sing current it changes both the attenuation and phase shift ofthe feedback loop in mutually aiding manner to permit an increase offeedback and a controlled sing condition. The current IESDOXI? sivedevice can advantageously be a thermistor arranged to be heated undercontrol of the sing current.

The nature and objects of the invention will appear more fully from thefollowing detailed description in connection with the drawings, inwhich:

Fig. 1 is a schematic circuit diagram of a complete amplifier circuitincorporating the invention in one form;

Figs. 2, 3 and 4 show modified types of network that may be substitutedin the circuit of Fig. l; and

Figs. 5 to' 17, inclusive, show graphs to be referred to in thedescription.

Fig. 1 is intended to represent by way of illustration a typical broadband feedback amplifier such as might be used as a repeater in amultiplex carrier telephon system, a television system, or the like. Itis shown as comprising three stages represented by the tubes I, 2, and 3with an input transformer 4 and output transformer 5 for coupling tosections of line and with a feedback network 6. The first interstagenetwork is shown at I and the second interstage network at 8. The

latter is represented as a network of the bridged- T type of symmetricalproportions. It includes as the series arm a resistance I and twocapacities II, II. The plate circuit branch comprises resistance It andparallel capacity ll. The grid circuit branch comprises resistance l andparallel capacity Hi. In a typical case the capacities ll, I2, II, andIt may all be equal; the resistances l3 and I5 may be equal; and theresistance It may have twice the magnitude of resistance II or IE.Bridged across at the center point is the thermistor Or other variablecontrol device Ill whose function it is to control the attenuation andphase shift characteristics of the interstage 8 in response to a singcurrent developed in the amplifier, as will be more fully disclosedhereinafter.

For purposes of simplicity, the battery supplies have been omitted fromthe circuit of Fig. 1. Also, it will be understood thatthe tubes wouldordinarily be pentodes in the type of system referred to. In general,the number of stages, type of feedback used and type of transmissionsystem are not critical, since the invention is capable of use invarious types of amplifiers, so that the circuit of Fig. 1 is to beregarded as illustrative rather than limiting.

Figs. 2 and 3 show for illustration modified types of interstage networkthat may be used at 8 in Fig. 1. In each of these modified types thethermistor 20 is provided with a bias for bringing its temperature to anormal operating value. In this way the thermistor is rendered moresensitive to small changes in heating current. In Fig. 2 this is done bytapping of! a small amount of heating current from plate supply resistor2| and passing this current conductively through the thermistor 20. InFig. 3, alternatively, a portion of the plate current supplied to thepreceding tube is used to heat a heater resistance 22 which isassociated in heat transfer relation to thermistor 20', both elementsbeing shown as included in a suitable enclosure 23 which may be heatinsulated to a suitable degree, if desired, to control the time lag. Thethermistor 20 may in this case be additional to thermistor 20' or, ifdesired, a single thermistor zn' may be used. In the Fig. 1 constructionthe thermistor 20 is illustrated as heated only by the high frequencysing current flowing in the amplifier circuit. In the cases where athermistor bias is used the thermistor is heated by the steady biascurrent as well as by the sing current. A

Fig. 4 shows an alternative manner for controlling the thermistor 20 inwhich a constant resistance network 25 is connected to a point in the.feedback network I and the current transmitted through the network 25is applied to a heater 22. Except for the configuration of theinterstage 8 and the network 25 the circuit may be in accordance withFigs. 8 and 9 of my prior patent referred to, replacing the lower of thetwo 115- ohm resistances shown in Fig. 9 by the input impedance of thenetwork 25 which is made to have the value oi. 115 ohms. In this casethe sing current circulating in the feedback loop is used to vary theresistance of the thermistor 20 by flowing through resistance 22associated with the thermistor 20 in such a way as to heatthe latter.Network 25 may have any desired frequency characteristic and may, forexample, highly attenuate current of a frequency in the neighborhood ofthe upper edge of the used band or currents of frequencies in the bandand for a considerable range above the band to insure against operationof the equalizer by any except currents of the intended frequencies.

Fig. 8 shows a polar plot (dotted curve) of an absolutely stableamplifier designed in accordance with the disclosure in my'ampliflerpatent referred to, while the solid curve shows a Nyquist stability orconditional stability characteristic. The p value of the latter is shownas much greater and it has been recognized that this offered thepossibility of a valuable improvement in amplifier operation providedthe additional amount of feedback could be obtained with reliableoperation in other respects. The solid curve crosses the zero phase axisat three points representing three frequencies ii, In and ,f: inascending order. One difiiculty in attempting to operate withconditional stability has been that as the envelope expands or contractswith the building up or dying down of tube gain, there is a danger thateither the h or f: cross-over might pass through the 1, 0 point causingthe amplifier to remain permanently in a sing condition with acorrespondingly low value of i s]. This could happen, for example, whenthe amplifier is turned on and the gain builds up from zero or again asthe tubes age and lose gain.

The present invention completely obviates this difficulty for theamplifier is made to have unconditional stability at all lower gainsthan that required to produce a sing at or near the frequency I: and thecross-overs at ii and I: do not exist until a sing is definitelyestablished at some frequency near Is. This is represented by the curvesin Figs. 5 to 8 which show how the polar diagram grows as the amplifieris turned on and the gain increases. In Fig. 5 the circuit hasunconditionai stability. In Fig. 6 the circuit is just on the point ofsinging at a frequency higher than 11 or is. In Fig. 7 the sing has beenestablished and the envelope is beginning to be deformed by thethermistor controlled network to contribute more favorable gain andphase shift for changing over to conditional stability. In Fig. 8 thesolid curve has looped over, giving the characteristic conditionalstability case. If the tube gain is lowered the curve shapes change inthe reverse direction, that is, in the order from Fig. 8 to Fig. 5.

As an aid to determining the design requirements of the network 8 inrelation to the rest of the amplifier some general discussion will begiven with special reference to Figs. 9, 10, and 11. In each of thesefigures the curve 01, Bi, C1, D, E, F, and G is the characteristic of anunconditionally stable amplifler as developed in my amplifier patentreferred to. The curve F, I", G defines the high frequency asymptote andthe portion D, E, F shows the optimum shape of the characteristic as itapproaches and merges with the high frequency asymptote. As the curvesare drawn in these three figures, a gain margin x1 and a phase margin Yare indicated as is usual in the design of completely stable amplifiers.The position of the limit F, F, G is determined by the available tubegains up to the frequency at which the parasitic capacities becomecontrolling and it may be assumed as a matter of basic. design that theportion of the characteristic E, F, G as determined by the teachings ofmy amplifier patent gives the most advantageous shape for securingmaximum feedback. For simplicity it will be assumed that this portion ofthe characteristic should be the same for either the unconditionally orthe conditionally stable design. It remains, therefore, to determinewhat type of shaping is possible at lower frequencies to secure maximumfeedback with conditional or Nyquist stability while keeping theattenuation and phase unchanged overthe range E, F, G. Characteristicsfor a conditionally stable design are given on these three figures at02, B2, C2, D, E, F, G and in Fig. 9 areas A1 in the band and A: in thecut-off region are indicated respectively above and below thecharacteristic of complete stability.

It can be shown that for maximum feedback in the band, A1 should equalA: when plotted on a linear scale on the condition that both curvescoincide in the region E, F, G. This may be shown by the aid of Equation7 of my amplifier patent (2,123,178) which states the relation where Acand B are the attenuation and phase at w=wc and A is the attenuation atthe general point in. Let this equation be applied to the differencebetween the characteristics in Fig. 9.

Then A=0 beyond the point D in Fig. 9 since both characteristics followthe path D, E, F, G here.

Also, let me be chosen as a point beyond D. Then Ac=0 and the equationreduces to 2m. D A B;- T o dw since the integrand is zero beyond D. Butwe is always greater than (a in the new integrand and is much greater ifwe is well to the right of D. Thus we have approximately On the basis ofcoinciding attenuation characteristics to the right of D in Fig. 9, thislast expression shows that the phase characteristic in the neighborhoodof the cross-over, or at high frequencies generally, will not besubstantially affected by the change from unconditional to conditionalstability provided the total area under the attenuation characteristicsat lower frequencies is kept constant, or in other words, provided A1=A2when plotted on a linear frequency scale. Fig. 9 is plotted to alogarithmic frequency scale for convenience but it is obvious that witha linear scale the potential area A: can be very large, the limit beingreached when the line B202 comes vertically down to the horizontal axis.The greatest advantage from conditional stability is obtained,therefore, when 1320.: is steep and the margin X2 (Fig. 9) is small,giving the largest value for A2 and, consequently, for-Ar.

The attenuation and phase shift requirements of .the interstage network8 can be determined in the light of the foregoing discussion and fromthe given amplifier characteristics. To illustrate this, reference willbe made to Figs. 12 to 15. In Fig. 9 in order to make the demonstrationin regard to equality between areas A1 and A2 quite general, thecharacteristics assumed a no-sing condition. This was true also of thecharacteristics given in Figs. 10 and 11. Figs. 12 and 13 are similar toFigs. 9 and 10 but are for the case in which the margin X1 has beenreduced to zero, so that in the case of curves I and II the amplifier ison the point of starting to sing. It is desirable in the practice of thepresent invention'to allow this condition to be reached well below thefull gain of the tubes as indicated by curve I and also by Fig. 6. Thisallows the controls adequate range in which to operate and permits theconditionally stable characteristic to be fully established to maximumadvantage at the normal or expected operating point of the amplifier.Curve I is a normal unconditionally stable cut-oif characteristic forthe given instantaneous asymptote H1. Curve II is the correspondingabsolutely stable cut-off which is appropriate for the asmyptote H2which is realized in the circuit after the tubes have reached their fullgain. Curve III of Fig. 12 shows curve II deformed into a conditionallystable characteristic. The typical features of increased feedback in theuseful band, a region of very high cut-off rate just above the usefulband and a region 'of roughly constant gain somewhat further out, whichwere illustrated in Fig. 9, reappear here. Also, at still higherfrequencies from an. up to the asymptote Hz the curves II and IIIcoincide. Similarly, for the loop phase shift characteristics shown inFig. 13, there is a deformation of shape in the cut-off region ingoingfrom curve II to curve III but curves II and II merge and continue asone beyond an.

The curves in Fig. 14 show the changes in the attenuation characteristicof the network 8 which are brought about by variationof the element 20under control of the sing current, and the curves of Fig. 15 show thecorresponding changes in phase characteristic of the network. Since asing begins at the gain represented by curve I, the difference betweencurves I and III, less the change in tube gain, gives the requiredattenuation change to be effected by the network under control of thesing. This is given by curve III of Fig. 14. The dotted line curve showsa reasonable approximation for a practical design. Curve II of Fig. 14has been drawn as an aid to drawing the required characteristic III. IIshows the diiference between curves I and II and is what would berequired for the absolutely stable characteristic II (with zero margin).By not introducing the loss corresponding to II in the useful band theas gain is allowed to rise to the full value represented by III.

Curves III in Figs. 14 and 15, therefore, represent the required changein attenuation and phase characteristics which the network mustintroduce in response to the actuation of the thermistor or othercontrol 20, to permit the amplifier to work according to theassumed'specifications. The curve can be described generally as a broadbulge in attenuation extending from the upper edge of the useful band toapproximately the 'loss cross-over of the final amplifier. The

curve should have, preferably, a steep rise at the lower edge, near theuseful band, and a considerably more gentle trail-off near the upperedge. The accompanying phase shift changes appear in Fig. 15, includingthe introduction of some phase shift in the useful band and a relativelylarge amount in the cut-off region above the band.

The p attenuations corresponding to the characteristics given in Fig. 12are the attenuations of the entire loop including N ('7), equalizer 8and the feedback impedance Z (6) while the characteristic III of Fig. 14is the attenuation bulge that must b inserted under contro1 of thevariable element 28; so that with the type of circuit given in Fig. 1this bulge must be put in by the equalizer 8 alone. It is, of course,possible to apportion the total attenuation differently. The equalizer 8can introduce a normal attenuation and phase plus a controlled variableattenuation and phase or two different networks may be used forseparately contributing the normal and the variable componentsrespectively. Alternatively.

Curve the variable component can be introduced partly at one point inthe loop and partly at some other point, although from the standpoint ofsimplicity of design it is better to provide a single control where asui'flcient degree of change can be effected by a single control. Withthe type of network shown at I there is suiilcient frequencydiscrimination between signal and sing components so that only thelatter component heats the thermistor control element 20 and as thiselement varies in resistance the attenuation and phase of the network inthe cut-oi! ran e both vary progressively in the general manner shown inFigs. 14 and 15. Equalizer I also contributes to the normal asattenuation required to give the absolutely stable characteristic I ofFig. 12.

While for the purpose of achieving maximum value of feedback factor inthe useful band the invention provides for reshaping the m8characteristic in the high frequency cut-off region as has beendescribed, it is pointed out that some advantage can be gained fromcontrol of the loop gain and phase shift without going so far as toreshape the loop feedback characteristic in this region. Consider, forexample, the case of a completely stable amplifier design where the gainmargin X1 (Fig. 9) is small so that it might be expected that in theintended use of the circuit there would be times when this gain marginmight be wiped out for certain times or under certain conditions. Thecircuit then comes into the condition illustrated by the diagram of Fig.6. By providing a network such as in the circuit figures of thedrawings, a sin current starting as a result of the disappearance of thegain margin would produce a helpful change in both attenuation and phasearound the loop such as to hold the sing to an innocuous level and allowthe feedback factor in the band to remain high. Also a permanent singcondition is'avoided and the circuit returns to stable condition whenthe assumed change that reduced the gain margin to zero disappears. Themethod of the invention is far more effective for this purpose than theflat gain control method of the prior art referred to earlier. Thismethod involving a simultaneous control of both attenuation and phase iswithin the invention even though there be no substantial reshaping ofthe loop characteristic in the high frequency cut-oil region.

An alternative way of specifying the equalizer loss characteristic willnow be given with special reference to the curves of Fig. 16. The loopgain characteristic V is associated with the high frequency asymptote Avand the loop gain characteristic VI representing an increase in tubegain over curve V has the asymptote Avr. The change in asymptotic gainis represented by dG and is supposed to be differentially small. Let theasymptotic gain have a slope of 612 decibels per octave. (In a typicalcoaxial line broad band amplifler 11:3.) Let the theoretical cut-oflcharacteristic near the zero gain axis have the slope 61: decibels peroctave. Go here is the parameter used in Equation 12, et seq., of UnitedStates Patent 2,123,178 above referred to and in a typical case may havea value of about /3. It can be regarded as specifying the phase marginin the region Just before the loss cross-over even when the finalcut-ofl curves are considerably deformed from the theoretical.)

With a logarithmic frequency scale, the interval du at no in octaves isoctaves. This is also the interval du at e. between the curves V and VIsince the breadth oi. the flat part of the ideal characteristic on alogarithmic frequency scale is fixed. The difference, therefore, betweenthe curves V and V1 is 61rd aG u n Further mi w. TI

and we is approximately the frequency of the controlled sing.

The total change between the characteristics V and V1 is equal to theJoint effect of the change in tube gain, (10, and the change in loss ofthe variable equalizer. This leads to a simple speciflcation of theequalizer characteristic. Thus in the range w. to lab, where the netchange is zero, the equalizer loss should be equal to the increase intube gain, dG. Below we the difference between curves V and VIcorresponds to an equalizer loss It (ldG Above up the equalizer lossshould diminish rapidly to zero, since the analysis assumes that thefull change in tube gain is applicable to improve the asymptote.

The corresponding equalizer characteristic is shown by Fig. 17. Strictlyspeaking, it applies only for differentially small changes in tube gain,but it should be roughly aplicable to gross changes also, if we take asuitable average value for the significant points, such as the frequencyof sing, lab, in the characteristic.

The area under the curve of Fig. 17 below a k (1 ;)w.dG

In accordance with the equations developed earlier, the phasecharacteristic in the neighborhood of the sing frequency will remainsubstantially unaltered if we replace the actual curve below us by anyother giving the same area. Thus, with this emendation the specificationjust developed for the equalizer characteristics can be applied toconditionally as well as unconditionally stable circuits.

What is claimed is:

i. A broad band negative feedback amplifier operating with controlledhigh frequency sing and having means in the feedback loop circuitcontrolled by the sing current for so modifying the loop transmissionphase and gain characteristics in the high frequency cut-oi! regionimmediately above the useful band as to increase the magnitude of thefeedback factor in the useful band to a higher value than the maximumvalue obtainable with unconditionally stable operation and the samevalue of tube gain.

2. A broad band negative feedback amplifier operating with controlledhigh frequency sing and having a variable equalizer included in thefeedback loop, said equalizer comprising a current dependent resistanceresponsive to the sing current, said resistance, in response to theinitiation of the sing current, changing the equalizer characteristic insuch manner as greatly to steepen the high frequency gain cut-oil. ofthe loop transmission characteristic immediately above the useful bandand produce a corresponding increase in feedback factor in the usefulband.

3. A broad band negative feedback amplifier having its loop gain andphase shift characteris= tics proportioned in known maner to provideunconditionally stable operation for low tube gains representing afraction of the total tube gain of the circuit whereby a high frequencysing sets in with increasing gain beyond said fractional value of gain,and means in the feedback loop operating in response to the initiationof the slug condition for limiting the sing amplitude to a relativelylow value and for modifying the shape of the gain and phase shiftcharacteristics of the ieedbackloop to convert the loop characteristicfrom the unconditionally stable type to the conditionally stable type.

4. A broad band negative feedback amplifier having its loop transmissioncharacteristic designed in known manner to provide unconditionallystable operation at low tube gains from near zero up to a value wellbelow the operating tube gain value, whereby a high frequency sing setsin with increase of tube gain beyond said low value, means to limit thesing amplitude to too low a value to interfere with operation of theamplifier in the utilized band, and means controlled by the sing currentin increasing from zero up to said limited amplitude for transformingthe loop transmission characteristicto provide a greater feedback ratioin the used band when the operating value of tube gain has been reachedthan could be obtained with the same tube gain and unconditionallystable loop characteristic.

5. In a broad band negative feedback amplifier, an impedance networkincluded in the feed back loop and comprising a current dependentresistance, said amplifier having a total 1001) transmissioncharacteristic including that of said network, designed in known mannerto provide unconditionally stable operation for all tube gains from nearzero up to some relatively low value comprising only a fractional partof the eventual operating tube gain, whereby a sing sets in withincreasing tube gain above said relatively low value at a frequency wellabove the used band, means to utilize the resulting sing current tocontrol the magnitude of said current dependent resistance, said networkin turn limiting the maximum amplitude of the sing current withincreasing tube gain to too low a. value to interfere with operation ofsaid amplifier in the utilized band, said network under control ofincreasing sing current below said maximum value operating to modify theloop gain and sive to energy traversing said loop for changing the loopcharacteristic from the completely stable to the conditionally stablestate and maintaining the loop in the stable condition throughout saidchange.

'7. A wave translating system having an amplifying path and a feedbackpath forming with the amplifying path a negative feedback loop, saidsystem having its gain and phase shift characteristics proportioned inknown manner to make said loop completely stable for low values ofamplifying path gain, said system developing a high frequency sing atoperating values of amplifying path gain, a network in said loopincluding a current dependent resistance, said network changing its lossand phase shift characteristics under control of changes in value ofsaid resistance, said resistance being effective in response to themagnitude of the high frequency sing current to cause the consequentchange of loss and phase shift of the network to vary both the loop gainand loop phase shift characteristics in a direction to prevent the singcurrent from rising above an unimportant small amplitude.

8. A negative feedback space discharge tube amplifier comprising meansmaintaining said amplifier completely stable at low values of tube phaseshift characteristics in such sense as to reduce the sing margin in thehigh frequency cut-off interval and correspondingly increase the valueof the feedback factor in the used band.

6. A wave translating system comprising a space discharge tubeamplifying system, a feedback path forming therewith a negative feedbackloop, and means comprising a temperature dependent resistance ln saidloop having at less than normal tube gain a value rendering the loopcompletely stable and having atnormal tube gain a. value rendering theloop conditionally stable, said temperature dependent resistance beingrespongain while allowing said amplifier to develop a high frequencysing at high values of tube gain, means maintaining a phase marginagainst singing at all frequencies lower than said high frequency at allvalues of tube gain lower than the tube gain at which said highfrequency sing sets in, and means for causing the sing current tocontrol the loop gain and phase shift characteristics to cause operationwith conditional stability.

9. A broad band negative feedback amplifier having a loop characteristicof the unconditionally stable type but such a small phase margin as tobe liable to become unstable under operating conditions, said amplifierhaving a current responsive network of controllable attenuation andphase characteristics, and means operating in response to initiation ofa sing condition in said amplifier for' controlling the characteristicsof said network to in turn so modify the gain and phase characteristicsof the feedback loop as to maintain the sing current at negligibly lowamplitude and to maintain the loop gain within the utilized frequencyband at least as high as when operating with unconditional stability.

, 10. A negative feedback amplifier operating with conditional stabilityto secure a greater feedback factor in the used hand than is obtainablewith unconditionally stable operation comprising means for operatingsaid amplifier with unconditional stability at relatively low values oftube gain, means operative at somewhat higher tube gain for allowingsaid amplifier to start to sing at a. frequency much higher than anyutilized frequency while maintaining the circuit completely stable atall lower frequencies, and means utilizing the sing current to controlboth the loop gain and loop phase shift characteristics to convert thecircuit to conditionally stable operation with full tube gain whilemaintaining the amplitude of the sing at too low a. value to interferewith amplifier operation.

' HENDRIX W. BODE.

